A Study of Deterministic Jitter in Crystal Oscillators

Timing jitter is a concern in high frequency oscillators; the presence of timing jitter will degrade system performance in many high speed applications. In the first part of the paper, the authors have simulated the timing jitter due to CMOS device noise in a nine-stage CMOS differential ring oscillator, and a methodology to efficiently simulate timing jitter has been developed. Simulation results show that the variation of absolute jitter due to flicker noise has t-dependence while for white noise it has t/sup 0.5/-dependence; these are consistent with accepted theory. Two important parameters, cycle jitter and cycle-to-cycle jitter, used to describe jitter performance can be obtained from simulation. Simulation results are also compared with measurement results, and it is shown that simulation results are very close to measurement results. All these serve to verify the validity of this technique. In the second part of the paper, the authors have employed this methodology and investigated the timing jitter in silicon BJT/or SiGe HBT ECL ring oscillators, and they have shown that BJT/or SiGe HBT oscillators have lower jitter compared to their CMOS counterparts. The methodology described in the paper is also applicable to other types of clock generator and oscillators such as LC oscillators, as well as other kinds of noise source such as power supply and substrate noise.

We theoretically analyze the timing jitter due to both the carrier phase noise of laser-diode (LD) pulse sources and the Gordon-Haus effect in soliton transmission. A formula is derived for the timing jitter in terms of the carrier linewidth, one of the measurable parameters common to all types of LD pulse sources. The transmission distance restricted by the timing jitter is analyzed, and the carrier linewidths required for ultra-long distance and ultra-high speed soliton transmission are estimated as well. Recirculating loop experiments at 10 Gb/s are demonstrated using two pulse sources; a gain-switched DFB-LD and a sinusoidally driven monolithically integrated MQW-DFB-LD/MQW-EA modulator, which have different carrier linewidths due to their different pulse formation processes. The difference in the carrier linewidths of the two pulse sources is measured by the proposed technique which is based on the optical heterodyne method. The observed difference between the two pulse sources in terms of timing jitter accumulation and timing jitter reduction with optical bandpass filters for the two pulse sources well support the theoretical predictions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Timing jitter is a concern in high frequency timing circuits. Its presence can degrade system performance in many high-speed applications. In this paper, a new method for efficiently measuring timing jitter due to phase locked loops is described. Two important parameters, absolute jitter and cycle-to-cycle jitter, used to describe jitter performance can be analyzed. Simulation results for the measurement of jitter in phase locked loop using MATLAB SIMULINK are presented. The methodology described is also applicable to other types of clock generator and oscillators such as LC oscillators, as well as other kinds of noise source such as power supplies.

Synthetic Aperture Radar (SAR) is a coherent imaging radar. Hence, coherence is critical in SAR imaging. In a coherent system, several sources can degrade performance. Based on the HJ-1-C SAR system implementation and sensor characteristics, this study evaluates the effect of frequency stability and pulse-to-pulse timing jitter on the SAR coherent performance. A stable crystal oscillator with short-term stability of 101.010 / 5 msis used to generate the reference frequency by using a direct multiplier and divider. Azimuth ISLR degradation owing to the crystal oscillator phase noise is negligible. The standard deviation of the pulse-to-pulse timing jitter of HJ-1-C SAR is lower than 2ns (rms) and the azimuth random phase error in the synthetic aperture time slightly degrades the side lobe of the azimuth impulse response. The mathematical expressions and simulation results are presented and suggest that the coherent performance of the HJ-1-C SAR system meets the requirements of synthetic aperture radar imaging.

According to the analysis of phase noise and timing jitter in oscillators, a simple method of converting phase noise to timing jitter is presented and calculation examples are given. The result shows that the calculation timing jitter and measured value are very close. Therefore the timing jitter can be obtained by phase noise spectrum with some approximations.

Timing jitter as a key performance of single-photon avalanche diode (SPAD) detectors plays a significant role in determining the fast temporal response behavior of the SPAD device. Nevertheless, few analytic models are developed to directly calculate the characteristic of timing jitter for its modeling difficulty. In this paper, we propose a simple analytic modeling method, which can predict the temporal response of SPADs, without using time-consuming Monte Carlo simulation. Model investigation incorporates avalanche current, avalanche buildup time, and jitter tail under different conditions. Furthermore, the key model parameters provided by Geiger mode technology computer-aided design simulation allow an accurate prediction on timing jitter. Analytical results indicate that for an SPAD device structure with a shallow P+/N-well junction in a 0.18- $\mu \text{m}$ CMOS technology, the Gaussian peak response with about 110-ps full-width at half-maximum and the exponential jitter tail are in good agreement with the measured data, validating the accuracy, and feasibility of this modeling method.

An efficient ‘a priori’ model reduction for boundary element models

This paper explores the affect of phase modulation (PM), amplitude modulation (AM), and thermal noise on the rf spectrum, phase jitter, timing jitter, and frequency stability of femtosecond lasers and other precision sources. Using these concepts we can suggest how some noise aspects of femtosecond pulsed lasers should scale.

Cognitive radio is an enabling technology, which is expected to lead to a more efficient utilization of the available spectral resources due to its flexibility and its ability to sense its spectral environment. Recently, spectrum sensing methods based on exploiting the cyclostationary characteristics of communication signals have been drawing interest. In practice, imperfections in the signal generation or reception may affect the cyclic statistics of a signal of interest, leading to a degradation in the performance of cyclostationarity-exploiting spectrum sensing schemes based on an ideal signal model. A typical source of imperfection is random timing jitter, which can occur at the transmitter side, most notably in the form of pulse timing jitter for digitally modulated signals, or at the receiver side in the form of sampling jitter. In this work, we explore the effect of randomtiming jitter on the second order cyclostationary statistics of wide sense cyclostationary signals. General analytical expressions are derived for the cyclic statistics of signals in the presence of sampling and pulse timing jitter and specific results are provided for cases of practical interest. Subsequently, the effect of the both jitter types on a cyclostationary-based spectrum sensing algorithm is investigated via simulations.

A technique to enhance the stability of optical pulse source has been proposed that employs a specific length of unpumped erbium doped fiber. Two types of pulse sources are used one after the other, one of them is a 10 GHz mode locked laser and the other is a gain switched DFB laser diode with the repetition rate of 2 GHz. A 3-m erbium doped fiber is consolidated outside the cavity of the pulse sources so as to form strong standing waves, resulting into enhanced spatial hole burning effect. As a result, the phase noise of the pulse source is suppressed, whereas the possible undesired changes in the attributes of the pulse source are also nullified because we have designed the setup outside the cavity of the pulse source. Consequently, the timing jitter of the pulse source is reduced significantly.

In this paper, jitter due to both capacitive and inductive coupling is studied. Maximum frequency of driving signal on a wire is limited by its input rise time, fall time, pulse width, and the coupling effect from its neighbors. The analytical expressions to estimate the deterministic jitter time due to these effects are presented. The estimation is based on the fastest and slowest approximation of the signal waveform components. Also, we have extracted the eye opening parameters of the eye diagram. The inductance effects significance is shown on eye opening and jitter time. The 45nm technology is used for estimating the horizontal and vertical eye opening and jitter time. The presented formula is compared with the simulations for some cases and it shows good agreements.

The methods to reduce phase noise of crystal oscillators are presented and analyzed in the paper. According to analysis of Leeson formula, phase noise has a direct relation with noise factor F, corner frequency f c and loaded quality factor Q L . Based on the method of reducing phase noise by improving Q L , the formula of Q L is derived by analysis of Pierce oscillator circuit and simulated by MATLAB. According to the simulation result, we can draw a conclusion that Q L is explicitly related to circuit parameters. Based on this conclusion, phase noise of a Pierce crystal oscillator is simulated and analyzed by the Agilent Advanced Design System. The simulated phase noise results are reduced by adjusting circuit parameter. A design of the prototype 120 MHz Pierce crystal oscillator is presented and the experiments are carried out. The measured near carrier frequency phase noise can achieve −100 dBc/Hz@10Hz and −132 dBc/Hz@100Hz. The simulated and experimental results show that it is feasible to design low phase noise crystal oscillator based on improving Q L .

The numerical simulation of fractured-vuggy reservoirs has received much attention in the past years, because of the significant contribution of fractured-vuggy reservoirs to the oil and gas reserves and productions. In this paper, an efficient hybrid method is proposed to simulate two phase flow in the fractured-vuggy reservoirs with multiple-length scaled fractures and vugs, which cannot be easily modeled by only the continuum models or discrete models. In this hybrid model, small fractures and vugs are modeled by a continuum model, and long fractures are modeled by the embedded discrete fracture model. Firstly, the coarse grid system is made according to the structure characteristics of fractures and vugs. Then, the discrete fracture-vug model (DFVN) is implemented in each coarse grid to calculate equivalent permeability tensor based on homogenization theory, and an analytical procedure is implemented to obtain a pseudo relative permeability curves for each grid containing fractures and cavities. The long fractures are embedded in homogenized media system. After that, an efficient numerical simulator is devised to solve the coupled system of long fracture and homogenized media based on mimetic finite difference method. At last, several numerical examples have been shown to verify the validity and accuracy of the hybrid model.

To cool a high-pressure gas turbine blade, many rows of cooling holes with different arrangements and configurations are manufactured to achieve higher cooling effect and lower aerodynamic loss. To evaluate the heat transfer and film cooling effect in the full-cooled turbine blade, efficient numerical simulations are required in the design and performance optimization processes. From the view of numerical accuracy, the structured grids have to be employed because of higher resolution in flow and heat transfer than the unstructured grids. Because many splitting, attaching and merging manipulations are involved in meshing the cooling features and curved boundaries, it is very complex and time-consuming for a researcher to generate multi-block structured grids for a full-cooled gas turbine blade. As a result, in the industrial applications, almost all researchers preferred to generate unstructured grids instead of structured grids for the full-cooled blade. Unlike the previous research, the aim of this study is to apply the Background-Grid Based Mapping (BGBM) method proposed in Part I to generate multi-block structured grids for a full-cooled gas turbine vane. With the strategy of BGBM method, meshes were conveniently generated in the computational space with simple geometrical features and plain interfaces, and then were mapped back into physical space to obtain the multi-block structured grids which can be used for numerical simulations. With the experimental data, the present numerical methods and BGBM strategy were carefully validated. Then, the flow and film cooling performance in the full-cooled NASA GE-E3 nozzle guided vane were numerically investigated. The effects of coolant mass flow rate and land extensions on film cooling effectiveness were discussed. The results show that film cooling effectiveness near the stagnation point is the lowest and film cooling effectiveness on the pressure side is slightly higher than that on the suction side. When the coolant mass flow rate increases up to the value of 1.5 design flow, the relative outflow mass flow rates of cooling hole arrays and slots are no longer affected by the increase of the coolant flow rate. At half design flow, the outflow mass flow rates of No.5 hole-array to No.10 hole-array are almost zero, and the area-averaged film cooling effectiveness on vane surface is as low as 0.268. Compared with the cases of half design flow and double design flow, better film cooling performance is obtained in the cases of design flow and 1.5 design flow. Compared with the vane without lands, the area-average cooling effectiveness on vane surface is slightly higher for the vane with lands. Land extensions have a considerable influence on film cooling performance in the cutback region.

Summary Differential Acoustical Resonance Spectroscopy (DARS) has been developed to estimate the elastic properties of rock samples at kilohertz frequency range. The laboratory technique, which is based on a perturbation theory, measures the resonance frequencies of the resonator cavity with and without a test sample, and utilizes the resonant frequency shift to estimate the acoustic properties of the loaded sample. In order to better understand the operation mechanism of DARS, it is important to develop an accurate and efficient numerical simulation. This study presents a new multi-physics model for simulating the acoustic pressure field and identifying resonance frequencies of the DARS system through a standard finite element approach. The multi-physics numerical model is validated by using extensive experiment data for the empty cavity at three different resonance modes. It shows that the acoustic pressure fields and resonance frequencies are in fairly good agreement with the experiment data. Using simulated resonance frequencies with the newly developed numerical model, the DARS-estimated compressibility and density of the synthetic samples are very close to their true values. The numerical model is conducive to understanding the process of DARS, and can be used in the future for optimizing the low-frequency measurement technique.